Superposition de calques monochromes d'opacités variables

07/13/2017
by   Alexandre Bali, et al.
0

For a monochrome layer x of opacity 0< o_x<1 placed on another monochrome layer of opacity 1, the result given by the standard formula is Π( C_φ)=1+∑_n=1^2(2-n-(-1)^no_χ(φ+1))(χ(n+φ-1)-o_χ(n+φ-1)), the formula being of course explained in detail in this paper. We will eventually deduce a very simple theorem, generalize it and then see its validity with alternative formulas to this standard containing the same main properties here exposed.

READ FULL TEXT

page 1

page 2

page 3

02/11/2019

About the unification type of simple symmetric modal logics

The unification problem in a normal modal logic is to determine, given a...
01/03/2020

Bounds on the size of PC and URC formulas

In this paper we investigate CNF formulas, for which the unit propagatio...
09/30/2020

A generalization of Krull-Webster's theory to higher order convex functions: multiple Γ-type functions

We provide uniqueness and existence results for the eventually p-convex ...
09/17/2021

On the size of disjunctive formulas in the μ-calculus

A key result in the theory of the modal mu-calculus is the disjunctive n...
06/01/2018

Distance Distribution to Received Words in Reed-Solomon Codes

n this paper, we obtain an asymptotic formula for the number of codeword...
07/26/2022

A formalization of the change of variables formula for integrals in mathlib

We report on a formalization of the change of variables formula in integ...
01/22/2021

A Study of Continuous Vector Representationsfor Theorem Proving

Applying machine learning to mathematical terms and formulas requires a ...